SubjectsSubjects(version: 945)
Course, academic year 2014/2015
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Spatial Modelling - NMTP438
Title: Prostorové modelování
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2013 to 2014
Semester: summer
E-Credits: 8
Hours per week, examination: summer s.:4/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: doc. RNDr. Zbyněk Pawlas, Ph.D.
Class: M Mgr. PMSE
M Mgr. PMSE > Povinně volitelné
Classification: Mathematics > Probability and Statistics
Incompatibility : NSTP005
Pre-requisite : NMSA405
Interchangeability : NSTP005
Is pre-requisite for: NMTP541, NMST543
Is interchangeable with: NSTP005
Annotation -
Last update: doc. RNDr. Zbyněk Pawlas, Ph.D. (15.09.2013)
Random fields and spatial models on lattices, Markov random fields. Random measures on locally compact metric spaces, moment measures, Palm distribution. Point processes, stationarity, characteristics, Poisson process and other models of stationary point processes. Finite point processes with density, Markov point processes, inhomogeneous point processes, marked point processes.
Aim of the course -
Last update: doc. RNDr. Zbyněk Pawlas, Ph.D. (15.09.2013)

Introduce students into the basic methods for modelling of spatial data.

Literature -
Last update: doc. RNDr. Zbyněk Pawlas, Ph.D. (15.09.2013)

Cressie N.A.C.: Statistics for Spatial Data. Wiley, 1993.

Illian J., Penttinen A., Stoyan H., Stoyan D.: Statistical Analysis and Modelling of Spatial Point Patterns, Wiley, 2008.

Moller J., Waagepetersen R.P.: Statistical Inference and Simulation for Spatial Point Processes, Chapman&Hall/CRC, 2003.

Rataj J.: Bodové procesy, Karolinum, 2006.

Schabenberger O., Gotway C.: Statistical Models for Spatial Data Analysis. Chapman&Hall/CRC, 2005.

Teaching methods -
Last update: doc. RNDr. Zbyněk Pawlas, Ph.D. (25.02.2021)

Lecture+exercises.

Syllabus -
Last update: T_KPMS (24.04.2015)

1. spatial models on lattices, Markov random fields, Ising model, Gaussian models

2. random fields, variogram, autocovariance function

3. random measures, existence, weak and vague convergence

4. point processes, Poisson process and other examples, moment measures, Palm distribution

5. stationary point processes, Cox process, cluster processes, hard-core point processes

6. finite point processes with density, Markov point processes

7. nonhomogeneous point process, marked point processes, marking models

 
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